The police denied they fired rubber bullets or tear gas at the protesters.
People assist an injured student as Dhaka University students protesters gather during the eight-day protest demanding safer roads.Thousands of angry young people protested in Bangladesh's capital on Sunday to demand safer streets.
Bangladesh Prime Minister Sheikh Hasina urged students to go home as police fired tear gas at teenage protesters during an eighth day of unprecedented demonstrations over road safety which have paralysed parts of Dhaka.
Activists say at least four people have been injured.
The demonstrating students have stopped thousands of vehicles during the protests, including those of top officials, checking if the cars were registered and the drivers licensed.
In Rajshahi, students of different schools and colleges gathered at Zero Point at Saheb Bazar of the city around 1030 hrs protesting the attack on students during their demonstrations and seeking safer roads.
The police detained three persons after dispersing the agitating students using tear gas shells.
Zia's party has formally extended its support to the protesters, but Hasina has also reached out to the demonstrators by pledging to improve road safety.
Images and photos of the attacks on students allegedly by the ruling party activists have flooded the social media, prompting renewed outrage.
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Law Minister Anisul Huq told a separate briefing that if police investigations found drivers to have deliberately caused accidents to kill someone, they would face death penalty under the country's penal code.
Activists have also taken to social media in droves to call on local and global media organisations to cover the story.
They also blocked roads, only letting emergency vehicles through, and the Government has threatened to get tougher if the protests become too disruptive. Local media have blamed groups linked to the Awami League.
The protests come just months before general elections scheduled for December and follow another series of protests in Dhaka this past spring.
It is common in Bangladesh for people to drive vehicles without a valid licence.
It was not immediately clear how many people may have been injured.
"We are deeply concerned about the reports of violence and call on all for calm", the United Nations resident coordinator Bangladesh Mia Seppo said.
Bangladesh police yesterday began cracking down on unsafe driving.
All the telecommunications companies were directed to stop 3G and 4G services for a total period of 24 hours on late Saturday, the English-language Dhaka Tribune reported.
Dhaka-Mawa Bus Owners' Welfare Association president Ali Akbar said they were afraid to run their buses for possible vandalism.